Re: Single or Double angle bending member

• To: seaint(--nospam--at)seaint.org
• Subject: Re: Single or Double angle bending member
• From: "Jordan Truesdell, PE" <seaint1(--nospam--at)truesdellengineering.com>
• Date: Fri, 29 Apr 2005 09:05:21 -0400
```Will Haynes wrote:

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I see that torsion must be checked in the boundary stability of the lintel angle, but for the design of the angle, hopefully the vertical leg will not have much differential rotation. And the differential rotation is what will induce the torsional shear stresses. I can see there being bending in the vertical leg from it resisting torsion, the same type of bending induced in the horizontal leg from transferring the weight of the block to the vertical leg.
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Maybe there is a small amount of rotation difference of the angle between anchor locations. But I don't think you have to design for the full torsion, only that which overcomes the normal friction between the block and the horizontal leg.
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How many loose brick lintel angles have you ever seen? If torsion was such a large factor, wouldn't the angles twist right out? I'm not saying disregard it as a stability check, but I'm not sure if it is a big design issue. I wouldn't know where to start designing an angle for torsion either.
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Will

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The problem is that the center of the application of force of brick is 2" off the face of the leg of a typical 3.5" angle, so take your vertical force x 2" to get your torsion. Now, will this really happen? Probably not - the brick is more likely to sag a bit, and the application of force would shift back towards the leg, but that' would be a non-conservative assumption. Since the shear center of an angle runs through the center of the vertical leg, and angles have such low polar moments, you can see "real" torsion. Now, the ends are generally fixed by the weight of the brick above, which is a mitigating factor, as is the L/600 deflection criteria that is used for design. Stress rarely controls a brick angle design. I do know of cases where torsion was not taken into account for a beam with a bottom flange extension plate intended to support a brick facade - it rotated very badly.
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It could be worse, it could be a channel - their shear centers are behind the web, so you can't physically load a channel by itself through its shear center and you always end up with some torsional component.
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And, yes, torsion is a pain. Most texts spend all their effort on the determinate form on solution, which is typically a fixed-free round bar, with the advanced sections looking at non-circular sections. Rarely do they discuss warping in any useful way, and usually there is little or no discussion of a distributed force (most are point applications of loads, as for transmission shafts or eccentric linkages). The discrete forms of equations get ugly quickly - take a look at Tables 21 and 22 in Roark for examples - and they're just for point-torques, not distributed. Even Roark doesn't have distributed torque equations for thin walled sections. (Actually, I don't think it has it for circular members either.)
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Jordan

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